Problem: Simplify the following expression: $x = \dfrac{r^2 + 15r + 56}{r + 7} $
Explanation: First factor the polynomial in the numerator. $ r^2 + 15r + 56 = (r + 7)(r + 8) $ So we can rewrite the expression as: $x = \dfrac{(r + 7)(r + 8)}{r + 7} $ We can divide the numerator and denominator by $(r + 7)$ on condition that $r \neq -7$ Therefore $x = r + 8; r \neq -7$